Currently, the Windows version only supports the Xbox 360 controller for Windows (both the wireless receiver and the wired controller). Support for other game controllers will follow.
On Mac and Linux, these USB controllers should work, too:

Thrustmaster Dual Analog

Logitech RumblePad

On Linux, the analog triggers of the Xbox 360 controller don’t work, which is a limitation of the SDL library, and is currently not fixable.